### Abstract

For n independent, identically distributed uniform points in [0, 1]^{d}, d ≥ 2, let L_{n} be the total distance from the origin to all the minimal points under the coordinatewise partial order (this is also the total length of the rooted edges of a minimal directed spanning tree on the given random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of L_{n}, and show that L_{n} satisfies a central limit theorem, unlike in the case d = 2.

Original language | English |
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Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Advances in Applied Probability |

Volume | 38 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2006 Mar 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Applied Mathematics

### Cite this

*Advances in Applied Probability*,

*38*(1), 1-30. https://doi.org/10.1239/aap/1143936137

}

*Advances in Applied Probability*, vol. 38, no. 1, pp. 1-30. https://doi.org/10.1239/aap/1143936137

**Rooted edges of a minimal directed spanning tree on random points.** / Bai, Z. D.; Lee, Sungchul; Penrose, Mathew D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Rooted edges of a minimal directed spanning tree on random points

AU - Bai, Z. D.

AU - Lee, Sungchul

AU - Penrose, Mathew D.

PY - 2006/3/1

Y1 - 2006/3/1

N2 - For n independent, identically distributed uniform points in [0, 1]d, d ≥ 2, let Ln be the total distance from the origin to all the minimal points under the coordinatewise partial order (this is also the total length of the rooted edges of a minimal directed spanning tree on the given random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of Ln, and show that Ln satisfies a central limit theorem, unlike in the case d = 2.

AB - For n independent, identically distributed uniform points in [0, 1]d, d ≥ 2, let Ln be the total distance from the origin to all the minimal points under the coordinatewise partial order (this is also the total length of the rooted edges of a minimal directed spanning tree on the given random points). For d ≥ 3, we establish the asymptotics of the mean and the variance of Ln, and show that Ln satisfies a central limit theorem, unlike in the case d = 2.

UR - http://www.scopus.com/inward/record.url?scp=33646119184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646119184&partnerID=8YFLogxK

U2 - 10.1239/aap/1143936137

DO - 10.1239/aap/1143936137

M3 - Article

AN - SCOPUS:33646119184

VL - 38

SP - 1

EP - 30

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 1

ER -